Applied Mathematics/Laplace Transforms

The Laplace transform is an integral transform which is widely used in physics and engineering. Laplace transform is denoted as .

The Laplace transform is named after mathematician and astronomer Pierre-Simon Laplace.


For a function f(t), using Napier's constant"e" and complex number "s", the Laplace transform F(s) is defined as follow:


The parameter s is a complex number:

  with real numbers σ and ω.

This   is the Laplace transform of f(t).

Examples of Laplace transformEdit

Examples of Laplace transform
function result of Laplace transform
  (n is natural number)  
  (Delta function)  
  (Heaviside function)  

Examples of calculationEdit

(1)Suppose   (C = constant)